Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

REFERENCES 67
where the subindices ‘u’ and ‘d’ denote the mass (M) and angular momentum
(J) of the upper and lower constituents, respectively, and the
constants and are introduced in the following way:
It can be readily proven analytically using formulas (6) and (7) that
and cannot assume simultaneously positive values [13], so the
equilibrium of two Kerr black holes possessing positive Komar masses is
impossible. However, the equilibrium states with positive Komar masses
of both constituents are possible when at least one of the constituents is
a superextreme object.
Formulas (4)–(7) give a complete exact solution of the double–Kerr
equilibrium problem.
5. TOWARDS THE ANALYSIS OF THE
MULTI–BLACK
HOLE EQUILIBRIUM STATES
It is very surprising that although the double–Kerr solution does not
admit equilibrium states of two Kerr black holes, already in the case
of three aligned Kerr black holes the gravitational equilibrium is possible
for the constituents with positive Komar masses [14]. The results
recently reported in [14] open some new horizons for the study of multi–
black hole equilibrium configurations, and one may expect new interesting
future findings in this area.
Acknowledgments
This work has been partially supported by CONACyT of Mexico
(project 34222–E) and by DGICyT of Spain (project PB96-1306).
References
[1] D. Kramer and G. Neugebauer, Phys. Lett. A75 (1980) 259.
[2] K. Oohara and H. Sato, Prog. Theor. Phys. 66 (1981) 1891.